Table of Contents
International Journal of Quality, Statistics, and Reliability
Volume 2012 (2012), Article ID 985152, 10 pages
Research Article

Nonparametric Confidence Limits of Quantile-Based Process Capability Indices

1Department of Mathematics and Statistics, University of Southern Maine, 96 Falmouth Street, Portland, ME 04104, USA
2College of Sciences, Ningbo University of Technology, Ningbo, Zhejiang 315211, China

Received 1 August 2011; Accepted 23 December 2011

Academic Editor: Suk joo Bae

Copyright © 2012 Cheng Peng and Jiaqing Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose an asymptotic nonparametric confidence interval for quantile-based process capability indices (PCIs) based on the superstructure CNp(u,v) modified from Cp(u,v) which contains the four basic PCIs, Cp, Cpk, Cpm, and Cpmk, as special cases. Since the asymptotic variance of the estimator for quantile-based PCIs involves the density function of the underlying process, the existing asymptotic results cannot be used directly to construct confidence limits for PCIs. To obtain a consistent estimator for the asymptotic variance of the estimated quantile-based PCIs, in this paper, we propose to use the kernel density estimator for the underlying process. Consequently, the confidence limits for PCIs are established based on the consistent estimates. A real-life example from manufacturing engineering is used to illustrate the implementation of the proposed methods. Simulation studies are also presented in this paper to compare the two quantile estimators that are used in the definition of PCIs.